The global helium (He) shortage is now one of the most pressing challenges for superconducting NMR/MRI magnets, both for manufacturers and users. In the last decade, helium price has quadrupled and the rise is expected to accelerate as the US Federal Helium Reserve rapidly depletes. The on-going liquid helium (LHe) crisis makes it urgent, and imperative than ever, to develop LHe-free NMR/MRI magnets, for which HTS has a definite and overwhelming edge over LTS. However, there is a critical technology that has yet been applied to the HTS magnet: persistent-mode operation that requires superconducting HTS-HTS joints in the magnet. In 2013, our collaborators, Korea University and SuperMag Inc., reported a fabrication method and successful test results of an REBCO- REBCO superconducting joint, for the first time in magnet technology history, at the 23rd International Magnet Technology Conference. This REBCO-REBCO joint, measured in a bath of liquid nitrogen (LN2) at 77 K, has a resistance of <10-15 ?, sufficiently small for persistent-mode NMR and MRI magnets. As the first step toward developing the next-generation, LHe-free, persistent-mode HTS NMR/MRI magnets, this 2-year R21 program applies this outstanding splicing achievement to build and operate the first-ever persistent-mode HTS magnets wound with REBCO tape. Two specific aims of this 2-year program are to: 1) design and build two LHe-free, persistent-mode REBCO magnets of two relevant sizes, an 83-mm/2.35-T for NMR and a 500-mm/0.1-T for MRI; and 2) operate the two magnets, first in LN2 at 77 K and next in solid nitrogen (SN2) in the range 10-30 K. The main focus of the program is to develop practical solutions for persistent-mode operation of HTS NMR/MRI magnet that can be operated under a solid cryogen (LHe-free) condition. We strongly believe that both LHe-free and persistent-mode features will make the HTS magnet an indispensable option in the next-generation NMR/MRI magnets. Successful completion of this 2-year R21 program will result in further development of key technologies for manufacturing LHe-free, persistent-mode HTS NMR/MRI magnets that have never been available to date. Undoubtedly, it will push forward the state-of-the-art HTS magnet technology, to the next level. Ultimately, this new technology will lead to affordable NMR magnets for research and economical diagnostic MRI magnets that benefit more people.